Knuth’s Generalization of McCarthy’s 91 Function

Abstract

Donald E. Knuth of Stanford University asks [63] for a “proof by computer” of a theorem about his generalization, involving real numbers, of John McCarthy’s 91 function. This case study explores a largely successful attempt to use ACL2 to meet Knuth’s challenge. Real numbers are dealt with by mechanically verifying results that are true, not only about the field of all real numbers, but also about every subfield of that field.